1. Field of the Invention
The present invention relates to a method of generating mask pattern data on a mask pattern to be transferred to a substrate, a method of manufacturing a photo mask, and a method of manufacturing a semiconductor device.
2. Description of the Related Art
With downsizing of a device pattern, there is a demand for obtaining a resolution close to a theoretical limit which depends on a wavelength of optical beam. To realize this demand, a variety of phase shift masks are proposed as masks. In addition, as an exposure method, there is proposed an oblique incidence illumination technique in which a light incident onto a mask is inclined from an optical axis by an angle which corresponds to the numerical aperture of an objection lens system of a projection exposure apparatus. There is proposed another exposure method in which a phase shift mask and an oblique incidence illumination are combined with each other.
Both of the phase shift mask and the oblique incidence illumination technique are intended to enhance a resolution by utilizing a phase difference between the adjacent patterns. With this technology, a high resolution can be obtained with respect to a highly periodic and simple pattern such as an L/S (Line-and-Space) pattern. However, a satisfactory resolution cannot be obtained with respect to a random pattern contained in a device pattern.
In recent years, there is proposed a mask obtained by arranging in a random pattern region an un-transferable auxiliary pattern which cannot be transferred on a substrate. Also, there is proposed an exposure method using the mask. For example, in Jpn. Pat. Appln. KOKAI Publication No. 7-140639, there is disclosed a mask for use in projection exposure using the oblique incidence illumination, wherein the mask includes a pattern to be transferred and an un-transferable pattern. In the case where the to-be-transferred pattern has periodicity (that is, in the case where the pattern is periodically arranged at a fixed pitch), an un-transferable auxiliary pattern or patterns are provided in such a manner that the periodicity is maintained. On the other hand, in the case where the to-be-transferred pattern does not have periodicity (that is, in the case where the pattern is arranged to be isolated), an un-transferable auxiliary pattern or patterns are provided in such a manner that a periodicity is imparted to the to-be-transferred pattern. When λ is defined as a wavelength of the illumination light and NA is a numerical aperture of the projection lens, in the case where the to-be-transferred pattern formed of a light transmitting section (or a light shielding section) has a periodicity and a width of the to-be-transferred pattern is equal to or greater than λ/2 NA, one or more un-transferable auxiliary patterns formed of a light transmitting section (or a light shielding section) are provided, at pitches of 0.8×λ/2 NA to 1.4×λ/2 NA from an edge of the mask transmitting section (or a light shielding section), at an end of the periodic disposition of the to-be-transferred pattern. On the other hand, in the case where the to-be-transferred pattern formed of a light transmitting section has no-periodicity and is thus isolated, and a width of the to-be-transferred pattern is equal to or greater than λ/2 NA, one or more un-transferable auxiliary patterns formed of a light transmitting section (or a light shielding section) are provided, at pitches of 0.8×λ/2 NA to 1.4×λ/2 NA from an edge of the pattern, at one side or both sides of the to-be-transferred pattern.
In the above prior art disclosed in Jpn. Pat. Appln. KOKAI Publication No. 7-140639, in the case where the pattern is formed at one type of comparatively simple pitches, the technology is effective. However, an actual device, for example, a select gate and its vicinity of a NAND-type flash memory (FIGS. 1 and 13), comprises patterns with a variety of pitches: a region p1 of a pattern with a fine periodicity, a region p2 of a pattern adjacent to the region p1 and having a periodicity longer than that of the region p1, and a region p3 of a pattern whose periodicity is longer than that of the region p2. Patterns whose lithography margin is insufficient and which is to be provided with an auxiliary pattern are line patterns 11 and 12 in FIG. 1 and line patterns 11, 12 and 8 in FIG. 13. In the patterns shown in, for example, FIG. 13, when the oblique incidence illumination is used, a line width variation in edge portions E1 and E2 of the line patterns 11 and 12 having lowest periodicity is large.
With the conventional method of adding an auxiliary pattern, it is impossible to determine how the auxiliary pattern is deposited with respect to a pattern with a complicated arrangement such as the line pattern 11 or 12.
In addition, in the pattern of the select gate of the NAND-type flash memory, as shown in FIG. 13, a contact portion locally exists. In other words, a region having more non-periodic patterns than other pattern regions exists. Thus, a low-resolution problem occurs. With the patterns shown in FIG. 13, a sufficient resolution margin cannot be obtained with respect to a local portion 10 of the line patterns 8 and 9.
As described above, in the prior art of improving the margin by adding an un-transferable auxiliary pattern, it is impossible to determine how an auxiliary pattern should be disposed. Hence, there has not been successfully solved the low-margin problem in a pattern region which requires downsizing, in particular, in a non-periodic pattern region in a cell region of a device.